From EP 1 191 814 A1 it is known to use a warped filter in a feedback adaptive filter approach, with the purpose of reducing howling or feedback, in the hearing aid. Also it is known to use the warped filtering technique for other applications, for instance including loudspeaker equalization, audio coding and adaptive feedback cancellation.
Further it has been proposed to use warped filtering in an online feed forward filter design approach in a hearing aid.
A regular FIR filter has the transfer functionH(z)=Σkhk(z−1)k delay line elements=z−1 
By replacing the delay elements with warped delay elements a warped FIR (WFIR) filter is obtainedF(z)=Σkgk(w−1)k delay line elements=w−1 where w=(1−λz−1)/(z−1−λ) as shown in FIG. 1.
A warped FIR filter (WFIR) is shown in FIG. 1 with warped delay line elements
      w          -      1        =                    z                  -          1                    -      λ              1      -              λ        ⁢                                  ⁢                  z                      -            1                              
The warping parameter 0≦λ<1 determines the amount of warping. The filter F(z) can be designed using regular FIR filter design techniques, e.g. the Fourier method, except the target frequencies are warped. A simple design example is shown in FIG. 2. Sample frequency is 20 kHz, λ=0.5. The target filter is a triangular bandpass filter (in absolute magnitude) with passband from 166 Hz to 332 Hz.
The FIR and WFIR filters are designed by similar approaches, the only difference being that the WFIR filter is designed on a prewarped frequency axis and the FIR filter being designed on a linear frequency axis. The result is easily seen from FIG. 2. The warped filter can match the target better due to more frequency resolution for low frequencies. The FIR filter can not match the steep slopes of the target curve at frequencies below 500 Hz. The filter resolution achieved by the FIR filter at 500 Hz is already achieved in the WFIR filter at 167 Hz, when X is set to 0.5 at a 20 kHz sampling frequency.
It is easily shown, that the frequency resolution of the warped filter is increased by a factor determined by the warping parameter, namely the expansion at 0 Hz:
      Δ    ⁢                  ⁢          f      ⁡              (        0        )              =            1      +      λ              1      -      λ      
For λ=0.5 this factor is 3, which means that a warped FIR filter has a resolution at low frequencies comparable to a FIR filter which is 3 times longer (at the expense of resolution at the high frequencies).
The benefit of warped filters is that they can tune their frequency resolution to any frequency region needed. If high resolution is needed at high frequencies the λ parameter must be set at for instance −0.5 relative to 0.5 when high resolution is wanted for low frequencies.
The cost for the increased flexibility is an increase in computational complexity. But when selecting λ appropriately, for instance to 0.5 the increase in computational complexity is low.
Lower average throughput delay is achieved when matching WFIR and FIR filters of the same computational complexity. And the throughput delay is only high at those frequencies, where high flexibility is needed. In symmetric FIR filters, the throughput delay is constant across frequency. The frequency dependent throughput delay of symmetric warped FIR filters is only dependent on the warping parameter λ. Thus the symmetric WFIR filter has a constant phase, even though the filter coefficients are changed (as long as λ is kept constant).
These known approaches do however not take advantage of the fall potential of the warped filter technique.